14 posts
138 posts
Re: raw meal homogenization
Hi,
I just realized my questions were based on a mistake.
Assuming the fresh meal composition is a pure (uncorrelated) white noise, mixing two samples separated by 1 hour, 1 minute or 1 day should be the same. Therefore the variance reduction does not depend on the delay but only on the number of samples included. (overlapping samples are excluded since this implies a correlation)
For the fun, let's make a simple model of your process.
Assume:
A(t) is the analysis of the fresh meal input to the silo
B(t) is the analysis of the mixed meal input to the silo
T is the residence time in the silo
then we have the relation:
B(t) = x*A(t) + y*B(t-T)
where x and y are the mix fractions and x+y=1 .
Computing the variance of both side of this equation leads to:
V(B) = x²*V(A) + y²*V(B)
or
V(B) = x²/(1-y²) V(A)
Taking the square root of the last equation gives you the variance reduction:
variance reduction = sqrt(x²/(1-y²))
It does not depend on the delay, because of the assumption of uncorrelated white noise.
138 posts
57 posts
Re: raw meal homogenization
Unfortunately, I don't think your reasoning will apply to reality.
Every equipment can be considered as a filter that will, at best, only reduce fluctuations that have frequencies higher or in the same order of magnitude than their residence time
The problem is that a 20 ton bin is indded very small for a kiln and will be emptied in a matter of a few minutes (unless you kiln is really really small that is). The residence time will be very short, so only high frequency i.e. fast fluctuations will be filtered.
Unfortunately, these fast fluctuations will probably already have been filtered by the previous equipment in the line (mainly the mill), so i doubt that you can actually decrease the standard deviation you observe on samples that are taken several hours apart.
For Mr. Lalbatros, the problem will be A(T) and B(t-T) will be severely correlated ;-)
Best regards,